Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
420 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 139 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. D4×Dic394 | C2 | semidirect |
| 3. #27161430 | C2 | semidirect |
| 4. #27161410 | C2 | semidirect |
| 5. #27161365 | C2 | semidirect |
| 6. #27161308 | C2 | semidirect |
| 7. #27161285 | C2 | semidirect |
| 8. #27161220 | C2 | semidirect |
| 9. C4×#15691347 | C2 | semidirect |
| 10. C2×#20263251 | C2 | semidirect |
| 11. C8×D4×C197 | C2 | semidirect |
| 83. Dic394 | #41 | semidirect |
| 96. D4×C197 | SD16 | semidirect |
| 128. C197 | #3298 | semidirect |
| 139. C8×D4 | D197 | semidirect |
| 217. D4 | #15691347 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Dic394 | 2 |
| #27161733 | 2 |
| #27161430 | 2 |
| #27161410 | 2 |
| #27161365 | 2 |
| #27161308 | 2 |
| #27161285 | 2 |
| #27161220 | 2 |
| C4×#15691347 | 2 |
| C2×#20263251 | 2 |
| C8×D4×C197 | 2 |
| #3298 | 197 |